Subject: The nature of continuum
Date: Thu, 08 Apr 2004 04:04:06 +0300
From: Dimi Chakalov <>
To: Chen Ning Yang <>,

Dear Professor Yang,

I wonder if you would consider posting your fundamental paper [Ref. 1] on LANL e-print archive. I think it could educate many young physicists. I personally lost many years  -- I mean, years -- with hopeless efforts to "understand" quantum mechanics, until I suddenly realized that I've tacitly assumed the following Gedankenexperiment:

Imagine that I can shrink the volume of my body down to the Planck scale, and can look at my wristwatch at all times. I can go down to this ultimate cut-off, since we use it in our calculations, and then get back to my usual size. My watch will be reading a continuous time variable, and the whole walk to the Planck scale and back to the scale of tables and chairs will take some finite time, as read by my watch.

Of course, we know that this is impossible, but the curious thing is that this tacit presumption of something that can go small/big along a *continual variable* is present in our calculations.

You showed that there is no such thing in current theoretical physics. The two realms, classical and quantum, are of totally different nature. There is no 'backbone' or 'common denominator' of the two worlds in today's theoretical physics. The reason why our calculations work is not known.

The late Jeeva Anandan stressed  [Ref. 2] that the "simplest, though dramatic, statement of the measurement problem in quantum theory is that quantum theory does not explain the occurrence of events. So, quantum theory does not explain the first thing we observe about the world around us."

Please do consider posting your paper on LANL e-print archive. I think everyone who talks about quantum physics and lives in the macro-world should read it. I'm afraid there is too much 'ornamental physics' [Ref. 3] in quantum gravity research. One of the biggest hurdles in background-free quantum gravity is the nature of time,

Theorists are doing all efforts to understand it, but I believe the crux of the issue is in that 'backbone' of the two worlds, which is not present in today's textbooks. It does exist 'out there' as physical reality, and we have to find it. I believe the best starting point is your paper. [Ref. 1]

With kindest regards,

Dimi Chakalov


[Ref. 1] Chen Ning Yang, Square Root of Minus One, Complex Phases and Erwin Schrödinger, in: Schrödinger: Centenary Celebration of a Polymath. (Proceedings of a conference held at Imperial College to celebrate the centenary of the birth of Erwin Schrödinger, March 31 - April 3, 1987.) Ed. by Clive W. Kilmister, Cambridge University Press, New Rochelle, 1987.

[Ref. 2] Jeeva Anandan, Quantum Measurement Problem and the Possible Role of  the Gravitational Field, Found. Phys. 29, 333-348 (1999).

[Ref. 3] Asher Peres, Klauderfest Guestbook,

"In February 1979 I started my first visit to Bell Labs, which was then a great national laboratory. (...) I was very happy at Bell Labs. Once I asked someone why I was treated so well to do just what was of interest to me. The answer: "We need people like you to improve the intellectual atmosphere. It's like putting flowers in the parking lot. This does not help parking, but this makes it more pleasant." Then one day, I met an Israeli physicist (solid state) who was surprised to see me there. He asked: Asher, what are you doing at Bell Labs? I answered: ornamental physics."

Note: I often receive email from theoretical physicists, who politely refuse to comment on my proposal for quantum gravity research, because they claim that cannot comment on some phenomenological theory that is not spelled out with math. As if there were some rigorous mathematical theory of quantum gravity, with which I should compete, in order to qualify for their professional criticism and suggestions.

Math is a language with which we express our thoughts. If they are unclear and contradictory, we will produce nothing but 'ornamental physics'.

First, the very notion of "point", with which we model an 'event', is initially wrong. Just like the case of the so-called collapse [Ref. 2], we do not know why our calculations work, despite the obvious error in the way we present the fundamental object called "point".

Consider this. In order to talk of 'spacetime', we need to identify timelike, lightlike, and spacelike distances (more from John L. Bell). If they fuse into some incomprehensible quantum mesh, there is no way we could recover the spacetime at the scale of tables and chairs: the common 'back bone' of classical and quantum worlds is not known (cf. my Gedankenexperiment above).

Think of a spacetime domain of finite dimensions, and start squeezing it toward the "point" at the Planck scale. I believe there is a consensus among physicists that at the final stage of reaching the Planck scale, the notion of spacetime would break down: there will be no difference between timelike, lightlike, and spacelike distances. The only thing we know about quantum fluctuations of spacetime metric is that they will kill the very notion of spacetime. Once you reach this dead-end, there is no way you could get back to the world of tables and chairs. For cosmological considerations, see the paradox of vacuum cleaner here.

Let's try to put some order in our thoughts about spacetime, and then will see what would be the proper math language.

Psychologically, there is a limit of constructing generalized concepts, due to the relation between the volume and the content of a concept, as explained here. Hence by 'spacetime' we refer to the most general properties of all physical objects. The volume of the concept of spacetime covers all conceivable physical objects, which have the common characteristics of being placed in some finite spacetime domain with three distances -- timelike, lightlike, and spacelike distances. Physicists cannot talk of spacetime of some 'empty space' devoid of any physical object: the question 'spacetime of what?' is crucial. Thus, if the physical content of the spacetime domain breaks down, the notion of spacetime is demolished as well. The spacetime is born with matter, and dies with dead matter at the Planck scale or the Planckian "time", just 10-43 sec "after" The Beginning.

Isn't it obvious that we need new ideas about spacetime? We cannot reject the considerations above; we have to amend them by adding a new kind of reality, and subsequently new kind of spacetime pertaining to this new kind of reality. First, we need something which will not break down by reaching the ultimate wall of Planck scale, and will allow us to get back home at the scale of tables and chairs. Secondly, we need to explain the phenomenon of transience, since it does work 'out there', as implied by the simple mathematical instruction 'shrink the volume of this sphere to approach zero'. We have learned how to mimic Mother Nature on a sheet of paper, now we have to zoom on the actual mechanism. With math. Otherwise our textbooks in QM and GR will never explain the occurrence of events, "the first thing we observe about the world around us", as stressed by the late Jeeva Anandan.

If you, my dear reader, don't know the math, please do not complain that I haven't provided it here. If you do know the math, please write a paper and rush it to Nature. I will read it and will zoom on every detail of your math with great scrutiny.

Please try first the 'square root of minus one' by Prof. Chen Ning Yang. Try also the insights of John Baez, The Square Root of Complex Conjugation - A Puzzle, dated October 24, 1997. He wrote, in plain English, "You don't need to tell me the answer. I already know what I think the answer is."

Isn't it amazing? John Baez is so good in math! I'm not. I tried to find the transition from classical to quantum regime in the biquaternion QM of Elio Conte, but nothing came out from this exercise. Besides, how would you formulate some theory of gravity in 3-D space with quaternions or biquaternions? Specifically, how would you keep the complex phase of quantum waves intact, to fix some 'back bone' for the transition from classical to quantum world and back? What kind of spacetime would be needed to describe the atemporal medium in both Einstein's GR and the standard QM? Where is the complex phase of the so-called gravitational waves? Can we find it in the bi-directional "talk" of matter and geometry?

Thank you for reading this, and good luck with your math.

D. Chakalov
April 25, 2004